Nonuniform sampling of bandlimited functions

IEEE Transactions on Information Theory

Volumn 54, Issue 8, 2008, Pages 3814-3819

  Shin, Chang Eon ^a   Lee, Mun Bae ^a   Rim, Kyung Soo ^a  

^a Sogang University   (South Korea)

Author keywords

Bandlimited function; Bandwidth; Convergence; Fourier transforms; Interpolation; Kadec's constant 1 4; Lagrange interpolation; Mathematics; Nonuniform sampling series expansion; Object recognition; Reflection; Robustness; Uniform convergence

Indexed keywords

BAND-LIMITED FUNCTIONS; BANDLIMITED FUNCTION; BANDWIDTH; CONVERGENCE; FOURIER TRANSFORMS; INTERPOLATION; KADEC'S CONSTANT 1/4; LAGRANGE INTERPOLATION; MATHEMATICS; NON-UNIFORM SAMPLING; NONUNIFORM SAMPLING SERIES EXPANSION; OBJECT RECOGNITION; REFLECTION; ROBUSTNESS; UNIFORM CONVERGENCE;

EID: 48849088405     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2008.926458     Document Type: Article

References (13)

1. A. Aldroubi and K. Gröchenig, "Nonuniform sampling and reconstruction in shift-invariant spaces," SIAM Rev., vol. 43, pp. 585-620, 2001.
2. W. Chen, S. Itoh, and J. Shiki, "Irregular sampling theorems forwavelet subspaces," IEEE Trans. Inf. Theory, vol. 44, no. 3, pp. 1131-1142, May 1998.
3. J. R. Higgins, "A sampling theorem for irregularly spaced sampling points," IEEE Trans. Inf. Theory, vol. IT-22, no. 5, pp. 621-622, Sep. 1976.
4. J. R. Higgins, Sampling Theory in Fourier and Signal Analysis. New York: Oxford Univ. Press, 1996.
5. G. Hinsen, "Abtastätze mit Unregelmäabigen Stützstellen: Rekonstructionsformeln, Konvergenzaussagen und Fehlerbetrachtungen," Ph.D. dissertation, Dept. Math., RWTH Aachen, Aachen, Germany, 1991.
6. G. Hinsen, "Explicit irregular sampling formulas," J. Comput. Appl. Math., vol. 40, pp. 177-198, 1992.
7. p-functions," J. Approx. Theory, vol. 72, pp. 346-364, 1993.
8. M. I. Kadec, "The exact value of the Paley-Wiener constant," Soviet Math. Dokl., vol. 5, pp. 559-561, 1964.
9. Korevaar, "An inequality for entire functions of exponential type," Nieuw Arch. Wisk., vol. 2, pp. 55-62, 1945.
10. N. Levinson, Gap and Density Theorems, ser. Amer. Math. Soc. Colloq. Pub. Series. New York: Amer. Math. Soc., 1940, vol. 26.
11. K. Seip, "An irregular sampling theorem for functions bandlimited in a generalized sense," SIAM J. Appl. Math., vol. 47, pp. 1112-1116, 1987.
12. R. M. Young, An Introduction to Nonharmonic Fourier Series. New York: Academic, 1980.
13. A. I. Zayed, Advances in Shannon's Sampling Theory. Boca Raton, FL: CRC Press, 1993.